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The C Standard, 6.2.5, paragraph 9 [ISO/IEC 9899:2011], states

A computation involving unsigned operands can never overflow, because a result that cannot be represented by the resulting unsigned integer type is reduced modulo the number that is one greater than the largest value that can be represented by the resulting type.

This behavior is more informally called unsigned integer wrapping. Unsigned integer operations can wrap if the resulting value cannot be represented by the underlying representation of the integer. The following table indicates which operators can result in wrapping:

Operator

Wrap

Operator

Wrap

Operator

Wrap

Operator

Wrap

+

Yes

-=

Yes

<<

Yes

<

No

-

Yes

*=

Yes

>>

No

>

No

*

Yes

/=

No

&

No

>=

No

/

No

%=

No

|

No

<=

No

%

No

<<=

Yes

^

No

==

No

++

Yes

>>=

No

~

No

!=

No

--

Yes

&=

No

!

No

&&

No

=

No

|=

No

un +

No

||

No

+=

Yes

^=

No

un -

Yes

?:

No

 

The following sections examine specific operations that are susceptible to unsigned integer wrap. When operating on integer types with less precision than int, integer promotions are applied. The usual arithmetic conversions may also be applied to (implicitly) convert operands to equivalent types before arithmetic operations are performed. Programmers should understand integer conversion rules before trying to implement secure arithmetic operations. (See INT02-C. Understand integer conversion rules.)

Integer values must not be allowed to wrap, especially if they are used in any of the following ways:

  • Integer operands of any pointer arithmetic, including array indexing
  • The assignment expression for the declaration of a variable length array
  • The postfix expression preceding square brackets [] or the expression in square brackets [] of a subscripted designation of an element of an array object
  • Function arguments of type size_t or rsize_t (for example, an argument to a memory allocation function)
  • In security-critical code

The C Standard defines arithmetic on atomic integer types as read-modify-write operations with the same representation as regular integer types. As a result, wrapping of atomic unsigned integers is identical to regular unsigned integers and should also be prevented or detected.

Addition

Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. This rule applies only to addition between two operands of arithmetic type. (See ARR37-C. Do not add or subtract an integer to a pointer to a non-array object and ARR30-C. Do not form or use out-of-bounds pointers or array subscripts.)

Incrementing is equivalent to adding 1.

Noncompliant Code Example

This noncompliant code example can result in an unsigned integer wrap during the addition of the unsigned operands ui_a and ui_b. If this behavior is unexpected, the resulting value may be used to allocate insufficient memory for a subsequent operation or in some other manner that can lead to an exploitable vulnerability.

Compliant Solution (Precondition Test)

This compliant solution performs a precondition test of the operands of the addition to guarantee there is no possibility of unsigned wrap:

Compliant Solution (Postcondition Test)

This compliant solution performs a postcondition test to ensure that the result of the unsigned addition operation usum is not less than the first operand:

Subtraction

Subtraction is between two operands of arithmetic type, two pointers to qualified or unqualified versions of compatible object types, or a pointer to an object type and an integer type. This rule applies only to subtraction between two operands of arithmetic type. (See ARR36-C. Do not subtract or compare two pointers that do not refer to the same array, ARR37-C. Do not add or subtract an integer to a pointer to a non-array object, and ARR30-C. Do not form or use out-of-bounds pointers or array subscripts for information about pointer subtraction.)

Decrementing is equivalent to subtracting 1.

Noncompliant Code Example

This noncompliant code example can result in an unsigned integer wrap during the subtraction of the unsigned operands ui_a and ui_b. If this behavior is unanticipated, it may lead to an exploitable vulnerability.

Compliant Solution (Precondition Test)

This compliant solution performs a precondition test of the unsigned operands of the subtraction operation to guarantee there is no possibility of unsigned wrap:

Compliant Solution (Postcondition Test)

This compliant solution performs a postcondition test that the result of the unsigned subtraction operation udiff is not greater than the minuend:

Multiplication

Multiplication is between two operands of arithmetic type.

Noncompliant Code Example

The Mozilla Foundation Security Advisory 2007-01 describes a heap buffer overflow vulnerability in the Mozilla Scalable Vector Graphics (SVG) viewer resulting from an unsigned integer wrap during the multiplication of the signed int value pen->num_vertices and the size_t value sizeof(cairo_pen_vertex_t) [VU#551436]. The signed int operand is converted to size_t prior to the multiplication operation so that the multiplication takes place between two size_t integers, which are unsigned. (See INT02-C. Understand integer conversion rules.)

The unsigned integer wrap can result in allocating memory of insufficient size.

Compliant Solution

This compliant solution tests the operands of the multiplication to guarantee that there is no unsigned integer wrap:

Exceptions

INT30-C-EX1: Unsigned integers can exhibit modulo behavior (wrapping) when necessary for the proper execution of the program. It is recommended that the variable declaration be clearly commented as supporting modulo behavior and that each operation on that integer also be clearly commented as supporting modulo behavior.

INT30-C-EX2: Checks for wraparound can be omitted when it can be determined at compile time that wraparound will not occur. As such, the following operations on unsigned integers require no validation:

  • Operations on two compile-time constants
  • Operations on a variable and 0 (except division or remainder by 0)
  • Subtracting any variable from its type's maximum; for example, any unsigned int may safely be subtracted from UINT_MAX
  • Multiplying any variable by 1
  • Division or remainder, as long as the divisor is nonzero
  • Right-shifting any type maximum by any number no larger than the type precision; for example, UINT_MAX >> x is valid as long as 0 <=  x < 32 (assuming that the precision of unsigned int is 32 bits)

INT30-C-EX3. The left-shift operator takes two operands of integer type. Unsigned left shift << can exhibit modulo behavior (wrapping).  This exception is provided because of common usage, because this behavior is usually expected by the programmer, and because the behavior is well defined. For examples of usage of the left-shift operator, see INT34-C. Do not shift an expression by a negative number of bits or by greater than or equal to the number of bits that exist in the operand.

Risk Assessment

Integer wrap can lead to buffer overflows and the execution of arbitrary code by an attacker.

Rule

Severity

Likelihood

Remediation Cost

Priority

Level

INT30-C

High

Likely

High

P9

L2

Automated Detection

Tool

Version

Checker

Description

Astrée17.04iinteger-overflowFully checked
CodeSonar4.4

ALLOC.SIZE.ADDOFLOW
ALLOC.SIZE.IOFLOW
ALLOC.SIZE.MULOFLOW
ALLOC.SIZE.SUBUFLOW
MISC.MEM.SIZE.ADDOFLOW
MISC.MEM.SIZE.BAD
MISC.MEM.SIZE.MULOFLOW
MISC.MEM.SIZE.SUBUFLOW

Addition overflow of allocation size
Integer overflow of allocation size
Multiplication overflow of allocation size
Subtraction underflow of allocation size
Addition overflow of size
Unreasonable size argument
Multiplication overflow of size
Subtraction underflow of size

Compass/ROSE

 

 

Can detect violations of this rule by ensuring that operations are checked for overflow before being performed (Be mindful of exception INT30-EX2 because it excuses many operations from requiring validation, including all the operations that would validate a potentially dangerous operation. For instance, adding two unsigned ints together requires validation involving subtracting one of the numbers from UINT_MAX, which itself requires no validation because it cannot wrap.)

Coverity2017.07INTEGER_OVERFLOWImplemented
Klocwork2017NUM.OVERFLOW
CWARN.NOEFFECT.OUTOFRANGE
 
LDRA tool suite9.5.6493 S, 494 SPartially implemented
Polyspace Bug FinderR2016aUnsigned integer overflowOverflow from operation between unsigned integers
PRQA QA-C9.3

2910 (C)
2911 (D)
2912 (A)
2913 (S)

Partially implemented
RuleChecker17.04iinteger-overflowFully checked

Related Vulnerabilities

CVE-2009-1385 results from a violation of this rule. The value performs an unchecked subtraction on the length of a buffer and then adds those many bytes of data to another buffer [xorl 2009]. This can cause a buffer overflow, which allows an attacker to execute arbitrary code.

A Linux Kernel vmsplice exploit, described by Rafal Wojtczuk [Wojtczuk 2008], documents a vulnerability and exploit arising from a buffer overflow (caused by unsigned integer wrapping).

Don Bailey [Bailey 2014] describes an unsigned integer wrap vulnerability in the LZO compression algorithm, which can be exploited in some implementations.

CVE-2014-4377 describes a vulnerability in iOS 7.1 resulting from a multiplication operation that wraps, producing an insufficiently small value to pass to a memory allocation routine, which is subsequently overflowed.

Search for vulnerabilities resulting from the violation of this rule on the CERT website.

Related Guidelines

Bibliography

[Bailey 2014]Raising Lazarus - The 20 Year Old Bug that Went to Mars
[Dowd 2006]Chapter 6, "C Language Issues" ("Arithmetic Boundary Conditions," pp. 211–223)
[ISO/IEC 9899:2011]Subclause 6.2.5, "Types"
[Seacord 2013b]Chapter 5, "Integer Security"
[Viega 2005]Section 5.2.7, "Integer Overflow"
[VU#551436] 
[Warren 2002]Chapter 2, "Basics"
[Wojtczuk 2008] 
[xorl 2009]"CVE-2009-1385: Linux Kernel E1000 Integer Underflow"

 


16 Comments

  1. Enforcing this rule is possible, but I'm a little hesitant to recommend it, because of how disruptive it would be (just how much addition, etc. would need to be protected).

    To enforce addition, one need merely check that any 'a + b' expr is preceded by a (max - b > a) expr. Subtraction, etc. are similar. There are probably many exceptions.

    Hm...building a Rose checker would be a useful exercise mainly because it will help us learn the exceptions to this rule. I suspect there are many more than we realize.

  2. Unary - can cause wrapping

    Also, so can division/modulo by a negative number ...

    1. All true, but those are technically signed int operations. So the 'surprise' behavior occurs in converting signed to unsigned & back.

      1. In that case, we should probably either not list them in the table, or mark them as capable of producing wrapping

  3. The second sentence under the heading Noncompliant Code Example in the Multiplication section states:

    The signed int operand is converted to unsigned int prior to the multiplication operation...

    I don't believe that is completely accurate. In a multiplication expression involving operands of types signed int and size_t, the signed int operand is converted to size_t. The type of size_t may be the same as either unsigned int or unsigned long in ILP32 but is the same as unsigned long in LP64 where sizeof(int) < sizeof(long).

    The vulnerability in the example is unrelated to the signed-ness of the type of the first operand but rather to the possibility of arithmetic overflow of the product of the two operands after the usual arithmetic conversions. The same vulnerability exists when both operands are of an unsigned integer type.

    1. I s/unsigned int/size_t/ in the paragraph. I believe overflow is possible on a 32- or 64-bit architecture (though for 64-bits, the sizeof() operation would have to return a really big size.) While the conversion occurs, it is not that important, as overflow is still possible, and easy on ILP32 if an attacker can specify num_vertices.

  4. I think there is a mistake in the Subtraction Compliant Solution (Post-condition Test)

    The second condition in the if statement should not be there.
    Eg:
    ui1 = 10, ui2 = 2
    udiff = 8
    It is still valid with 8 > 2.

    It looks like this was a copy paste mistake from the addition's compliant post-condition test.

    1. nice catch, thanks!

      1. Also the description just above that code.

        1. thanks, that should be fixed now too.

  5. I think that there's a minor think-o in the example given in the second to last item in INT32-EX2:

    " .... For instance, UINT_MAX >> x is valid as long as x < sizeof(unsigned int)"

    The comparison should be to the number of bits, not the sizeof.  Rather than faff around with CHAR_BITS or INT_BITS, which will probably only serve to obscure the main point, it might be best to just drop the example.

     

  6. The CS for Atomic Integers is somewhat misleading since it assumes that no writes have occurred between the atomic_fetch_add() and the subsequent atomic_load().  Given that the primary use case of atomics is environments where precisely that sort of thing can occur, safer (for selected values of "safer") might be something like (totally untested):

    A very minor nitpick: the variable naming in both the NCE and the CE appears to be wrong, as the (signed) type for ui_a doesn't seem to match the name (assuming ui_a is supposed to be a mnemonic for "an unsigned integer called a")

    1. Neil, as far as I am know the names are not meant to be mnemonic. I changed them from ui1 to ui_a, just to rid them of the 'l' (ell) and '1' (one) confusion factor.

  7. So the multiplication example in this rule does not parallel the multiplication example in INT32-C.  For this rule, we use a real world example but we provide only the portable solution and not the "store the product in twice as many bits solution".  Consequently, this rule does not require the UWIDTH() macro, which actually works with unsigned numbers right now.  Right now my feeling is that these two rules should be a little more parallel, and maybe we should include a twice the bits solution here, or remove it from INT32-C.